Micromechanical and Macroscopic Modelling (MMM)
Prof. Dr. Alexander Hartmaier
Developing innovative materials that meet the complex requirements of a diverse range of applications is only possible if the relation between their inner structure, i.e. the microstructure, and their properties is thoroughly understood. We derive such microstructure-property-relationships to predict macroscopic mechanical properties of materials, like strength, hardness, and fracture toughness, by employing the methods of computational materials science and multiscale modelling. To accomplish this, we typically start from macroscopic models that describe an engineering application or laboratory experiment and introduce information about mechanisms or material parameters that have been derived from more fundamental scales, see Figure 1 for an example about scalebridging in fracture modelling.
Macromodels typically do not consider the microstructure of a material explicitly, but are based on the idea of homogeneous material behaviour, which is a severe restriction of such models. However, they can be very useful to identify critical regions with high mechanical stresses and strains within a component or loading conditions that are potentially damaging. At such critical spots, a micromechanical model is employed that explicitly takes into account the local microstructure and mechanical conditions, taken from the macro simulation and applied as boundary conditions to the microstructure model. The microstructure in such micromechanical models is described by representative volume elements (RVE) that can be developed on different purpose-specific levels of detail, to represent either phases as homogeneous regions or individual grains within phases or even sub-structures within grains. Such micromechanical models serve mainly two purposes: Firstly, they yield insight into the critical deformation and failure mechanisms and how they depend on the microstructure and local thermal, mechanical, and chemical conditions of the ma1terial. Secondly, they provide the basis for macroscopic descriptions of material properties in form of flow rules as they are used in continuum plasticity. This latter step of developing macroscopic flow rules based on micromechanical models is termed homogenisation and can be used to take microstructural properties and mechanisms implicitly into account in macroscopic models of engineering problems. Figure 2 shows an example of a micromechanical model of a polycrystal that couples crystal plasticity and diffusion of hydrogen through the microstructure. Elastic strains change the driving force for hydrogen diffusion and segregation, which is quantified by ab-initio density functional theory calculations. Furthermore, plastic strains alter the density of hydrogen trapping sites. Thus, such a coupling of mechanics and diffusion is important to understand the nature of hydrogen distribution within a microstructure, which is an essential mechanism of hydrogen embrittlement.
One increasingly important aspect of research in the department Micromechanical and Macroscopic Modelling is to establish links between numerical modelling and experiment. As seen in Figure 6.2, our models yield results that can be directly compared to experiment, which enables (i) their direct experimental validation, and (ii) the parameterisation of micromechanical models by inverse fitting to experimental data. In view of the relatively large number of model parameters, the latter approach is currently a major thrust direction of our research.
The groups of the department are:
A list of research projects currently offered in the department of Micromechanical and Macroscopic Modelling (Prof. Hartmaier) can be found here